alexa Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission


Journal of Applied & Computational Mathematics

Author(s): P van den Driessche, James Watmough

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A precise definition of the basic reproduction number, R 0 , is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if R 0 < 1, then the disease free equilibrium is locally asymptotically stable; whereas if R 0 > 1, then it is unstable. Thus, R 0 is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for R 0 near one. This criterion, together with the definition of R 0 , is illustrated by treatment, multigroup, staged progression, multistrain and vector–host models and can be applied to more complex models. The results are significant for disease control.

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This article was published in Mathematical Biosciences and referenced in Journal of Applied & Computational Mathematics

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